In this article, a novel and efficient approach based on Lucas polynomials is introduced for solving three-dimensional mixed Volterra–Fredholm integral equations the two types (3D-MVFIEK2). This method transforms 3D-MVFIEK2 into system of linear algebraic equations. The error evaluation suggested scheme discussed. technique implemented in four examples to illustrate efficiency fulfillment appro...

This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...

The Fredholm–Volterra integral equation of the second kind with continuous kernels with respect to position and time, is solved numerically, using the Collocation and Galerkin methods. Also the error, in each case, is estimated.

Some New Uniqueness Results of Solutions for Fractional Volterra-Fredholm Integro-Differential Equations

in this paper, a numerical efficient method based on two-dimensional block-pulse functions (bpfs) is proposed to approximate a solution of the two-dimensional linear stochastic volterra-fredholm integral equation. finally the accuracy of this method will be shown by an example.

In this paper, a numerical efficient method based on two-dimensional block-pulse functions (BPFs) is proposed to approximate a solution of the two-dimensional linear stochastic Volterra-Fredholm integral equation. Finally the accuracy of this method will be shown by an example.

In this paper, we apply the homotopy perturbation method (HPM), modified method(MHPM), variational iteration (VIM), Adomian decomposition (ADM), and (MADM) to solve nonlinear mixed Volterra-Fredholm integral equations itssystem. We investigate approximate solution of equation its system via proposed methods. Thevalidity efficiency these methods are demonstrated through various numerical example...